Japanese Patent No. 4321411 (U.S. Pat. No. 7,063,080 B2) shows a system that performs a cylinder-by-cylinder air-fuel-ratio control. In the cylinder-by-cylinder air-fuel-ratio control, an air-fuel-ratio of each cylinder of an internal combustion engine is estimated based on a detection value of an air-fuel-ratio sensor. The air-fuel-ratio sensor detects the air-fuel-ratio at a specific timing for each cylinder. Based on the estimated air-fuel-ratio of each cylinder, the actual air-fuel-ratio of each cylinder is controlled. During an engine driving, a deviation in air-fuel-ratio detection timing is detected and the controller corrects the detection timing.
Specifically, it is determined whether the air-fuel-ratio detection timing deviates from a proper timing based on whether the variation of the estimated air-fuel-ratio between cylinders is large or whether increase-and-decrease directions of the fuel correction quantity and the estimated air-fuel-ratio are opposite to each other. When it is determined that the air-fuel-ratio detection timing deviates between cylinders, the air-fuel-ratio detection timing of each cylinder is corrected based on a relationship between a variation in estimated air-fuel-ratio of at least one cylinder and a variation in its corrected amount of fuel.
However, in the above cylinder-by-cylinder air-fuel-ratio control, when the increase-and-decrease direction of the fuel correction quantity and the estimated air-fuel-ratio becomes temporarily opposite to each other before the estimated air-fuel-ratio is converged, or when an estimation accuracy of the estimated air-fuel-ratio temporarily becomes deteriorated, it may be determined that the air-fuel-ratio detection timing deviates from a proper timing even though the air-fuel-ratio detection timing does not deviate.